The word ichthyosaur comes from two Greek roots. "ichthyos" means fish and "sauros" denotes lizards or reptiles. So ichthyosaurs are sometimes called "fish-lizards", although they are not phylogenetically considered lizards. The word "Ichthyopterygia" is a combination of "ichthyos" and "pteryx", the latter meaning a wing.

Usage of the word ichthyosaur in this page.

The word "ichthyosaur" is used as a common name for the animals belonging to the Ichthyopterygia, which contains the Ichthyosauria and basal forms (see the classification). Until recently, the Subclass Ichthyopterygia Owen, 1840 and Order Ichthyosauria Blainville, 1835 referred to the same natural group, and the name with the priority, the Ichthyosauria, has been preferred. So everybody is used to call the group "ichthyosaurs". However, Wiman (1929, 1933) actually restricted the extent of the Ichthyosauria over half a century ago, and so did Mazin (1981). Wiman's work has the priority over later studies, so the name Ichthyosauria should be used for the subset of the Ichthyopterygia that are more closely related to Ichthyosaurus than to Grippia. See Motani (in press b) for details. I still like to call the animals belonging to the Ichthyopterygia "ichthyosaurs" rather than cumbersome "ichthyopterygians".

How can you tell that ichthyosaurs are reptiles, not fish?

Well, there are many features but let me just mention a few examples. Features that indicate ichthyosaurs are tetrapods, not 'fish' (or non-tetrapod vertebrates)--The shoulder girdle and skull are connected in 'fish' , but not in tetrapods including ichthyosaurs. Also, the limbs of ichthyosaurs, although look like a fin from the outside, have stylopodial, zeugopodial, and autopodial skeleton just like in other tetrapods.Features that indicate that ichthyosaurs are reptiles among tetrapods--This could be a tricky question: if turtles turn out to be diapsids, the Sauria and Reptilia will become redundant, and ichthyosaurs will probably fall outside of the Reptilia=Sauria. So let me rephrase the question to "why ichthyosaurs are diapsids". Well, ichthyosaurs have a pair of openings on the skull roof called the upper temporal fenestra (or supratemporal fenestra), and this is a good diapsid feature. There is a postorbito-squamosal contact along this opening at least in basal forms, such as Utatsusaurus (see Motani et al., 1998).